License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.ICALP.2016.25
URN: urn:nbn:de:0030-drops-63049
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6304/
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Fluschnik, Till ; Hermelin, Danny ; Nichterlein, André ; Niedermeier, Rolf

Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems

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Abstract

Bodlaender et al.'s [Bodlaender/Jansen/Kratsch,2014] cross-composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability of cross-compositions. Our technique makes it possible to prove new no-polynomial-kernel results for a number of problems dealing with length-bounded cuts. Roughly speaking, our new technique combines the advantages of serial and parallel composition. In particular, answering an open question of Golovach and Thilikos [Golovach/Thilikos,2011], we show that, unless NP subseteq coNP/poly, the NP-hard Length-Bounded Edge-Cut problem (delete at most k edges such that the resulting graph has no s-t path of length shorter than l) parameterized by the combination of k and l has no polynomial-size problem kernel. Our framework applies to planar as well as directed variants of the basic problems and also applies to both edge and vertex deletion problems.

BibTeX - Entry

@InProceedings{fluschnik_et_al:LIPIcs:2016:6304,
  author =	{Till Fluschnik and Danny Hermelin and Andr{\'e} Nichterlein and Rolf Niedermeier},
  title =	{{Fractals for Kernelization Lower Bounds, With an Application to Length-Bounded Cut Problems}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6304},
  URN =		{urn:nbn:de:0030-drops-63049},
  doi =		{10.4230/LIPIcs.ICALP.2016.25},
  annote =	{Keywords: Parameterized complexity, polynomial-time data reduction, cross-compositions, lower bounds, graph modification problems, interdiction problems}
}

Keywords: Parameterized complexity, polynomial-time data reduction, cross-compositions, lower bounds, graph modification problems, interdiction problems
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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